{"uid":"cap_huKc-mr4qVwfPxaMnc33_","slug":"agent402-tools-prime-factorization-80753d9b","name":"agent402.tools Prime Factorization","description":"Find the prime factorization of an integer via trial division. Returns the list of prime factors (with repeats), a human-readable factorization string, whether the number is prime, and the count of distinct prime factors. Limit: numbers up to 10^15.","url":"https://agent402.tools/api/prime-factorize","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"number":{"type":"integer","description":"Integer > 1 to factorize (max 10^15)"}}},"responseSchema":{"type":"json","example":{"number":360,"factors":[2,2,2,3,3,5],"isPrime":false,"factorization":"2^3 × 3^2 × 5","distinctFactors":3}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.001","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.001/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.001","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.001","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_8h7lmldxaWC_hJ2K1TNZr","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.001","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes the prime factorization of an integer (up to 10^15) via trial division, returning prime factors, a readable factorization string, primality, and distinct factor count.","exampleAgentPrompt":"What is the prime factorization of 720720 — tell me the list of prime factors with repeats, the factorization string, whether it's prime, and how many distinct primes it has.","exampleUseCases":null,"resultDescription":"Returns a list of prime factors (with repetition), a human-readable factorization string (e.g. '2^4 × 3^2 × 5'), a boolean indicating whether the input is prime, and the count of distinct prime factors.","failureModes":["Number exceeds 10^15 limit — request rejected","Number is 1 or less — invalid input","Non-integer value supplied — schema validation error","Payment not included or insufficient — 402 Payment Required","Network timeout on very large near-prime numbers near the limit"],"whenToPreferThis":"Use this endpoint when you need to factorize a specific integer up to 10^15 and want both the raw list of prime factors and a formatted human-readable string, plus primality and distinct factor count in a single call. Prefer this over a general math API when you need trial-division factorization for number theory tasks, cryptographic analysis, or educational purposes.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T19:14:03.629Z","isFirstParty":false}